Let $f(x) = x^2-10x+9$. The function has $x$ intercepts at $1$ and $9$. For which values of $k$ does $f(x) = 2x + k$ have $1$ positive root and $1$ negative root?
My try: I got $f(x) = x^2-12x + 9 = k$. But now I noticed that I cannot factorise the expression. Can somebody please help me answer this question